\begin{abstract}
 We establish that mass conserving single terminal-linkage networks of chemical
 reactions admit positive equilibria regardless of the choice of reaction rate
 constants and network deficiency. 

Our proof uses a new convex-optimization approach for
analyzing the equilibrium behavior of networks of chemical reactions following
mass-action kinetics. We provide a fixed-point method to compute these
equilibria and report some of our numerical experiments. 
\end{abstract}


